Simulation paradoxes related to a fractional Brownian motion with small Hurst index - Vitalii Makogin (Modern Stochastics: Theory and Applications, 2016)
We consider the simulation of sample paths of a fractional Brownian motion with small values of the Hurst index and estimate the behavior of the expected maximum. We prove that, for each fixed N, the error of approximation $E\max _{t\in [0,1]}{B}^{H}(t)-E\max _{i=\overline{1,N}}{B}^{H}(i/N)$ grows rapidly to ∞ as the Hurst index tends to 0.